Frequency polygon

Frequency polygon is another way to show the information in a frequency table. It looks a little bit like a line graph. To make a frequency-polygon, you just need to plot a few points and then join the points by straight lines.
Frequency-polygon of a given frequency distribution can be drawn in two ways.
1) By using histogram 2) Without using histogram
After drawing a histogram, obtain the midpoints of each class. The midpoint of a class is the point in the middle of the class. So for instance, if I have a class “10 – 19”, then the midpoint is ( 10+19)/2 = 14.5. A class of “0 – 5” has a midpoint of 2.5. Join these mid points of the adjacent rectangles of the histogram by dotted line segments. Obtain the mid points of two class intervals of zero frequency on X-axis, one adjacent to the first, on its left and one adjacent to the last, on its right. These class-intervals are known as imagined class intervals.

Note : Sometimes imagined class intervals do not exist. For example marks obtained by the students in a test, we can not go below zero and beyond maximum marks on the two sides. In such cases extreme line-segments are partly drawn and are brought down vertically so that they meet with the vertical sides of first and the last rectangles.

Example without using histogram :

Age in years

Class marks

Frequency

0 - 2

1

2

2 - 4

3

4

4 - 6

5

6

6 - 8

7

8

8 -10

9

9

10- 12

11

6

12-14

13

5

14- 16

15

3

16- 18

17

1

Note: Class marks are obtained by adding the age in years and divide it by 2.